Department of Biostatistics Seminar/Workshop Series

Biostatistics Student Research Forum:

Spearman's Rank Correlation Adjusting for Covariates in Bivariate Survival Data

Svetlana K. Eden, Ph.D. Candidate, Department of Biostatistics

Vanderbilt University, School of Medicine

Many studies are interested in measuring associations between two right-censored time-to-event variables, sometimes called bivariate survival data. For example, researchers may want to assess associations between the times to cardiovascular disease for patients and their parents, or between times to events in twins. We develop a rank-based method to measure associations with and without adjusting for covariates. Our method fits separate semi-parametric models for the times to events conditional on covariates, obtains probability scale residuals (PSRs; Shepherd, Li, Liu [2016]) from these fitted models, and then computes the correlation of the PSRs. We show that without covariates, the correlation of PSRs equals Spearman's rank correlation for censored data. With covariates, the method is a natural extension of Spearman’s correlation to permit covariate adjustment and censoring. We propose ways to estimate the variance of our estimators and demonstrate their performance using simulations. We illustrate by investigating the association between times from treatment initiation to viral failure and regimen change among HIV-positive persons.